let N be with_non-empty_elements set ; :: thesis: for S being non empty IC-Ins-separated Mem-Struct of N
for p being PartState of S
for k, l being Nat holds (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S))
let S be non empty IC-Ins-separated Mem-Struct of N; :: thesis: for p being PartState of S
for k, l being Nat holds (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S))
let p be PartState of S; :: thesis: for k, l being Nat holds (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S))
let k, l be Nat; :: thesis: (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S))
dom (Start-At (k,S)) = {(IC )} by FUNCOP_1:13
.= dom (Start-At (l,S)) by FUNCOP_1:13 ;
hence (p +* (Start-At (k,S))) +* (Start-At (l,S)) = p +* (Start-At (l,S)) by FUNCT_4:74; :: thesis: verum